over which interval is the graph of the parent absolute value function $f(x) = |x|$ decreasing?\n$(-\\infty…

over which interval is the graph of the parent absolute value function $f(x) = |x|$ decreasing?\n$(-\\infty, \\infty)$\n$(-\\infty, 0)$\n$(-6, 0)$\n$(0, \\infty)$

over which interval is the graph of the parent absolute value function $f(x) = |x|$ decreasing?\n$(-\\infty, \\infty)$\n$(-\\infty, 0)$\n$(-6, 0)$\n$(0, \\infty)$

Answer

Explanation:

Step1: Define the piecewise function

The parent absolute value function can be written as a piecewise function: $$f(x) = \begin{cases} x & \text{if } x \geq 0 \ -x & \text{if } x < 0 \end{cases}$$

Step2: Analyze slope for each interval

For $x \geq 0$, the slope is $1$ (increasing). For $x < 0$, the slope is $-1$ (decreasing).

Step3: Match to interval options

The interval where the function decreases is all real numbers less than 0, which is $(-\infty, 0)$.

Answer:

$(-\infty, 0)$